Higher-order cumulants of the net-baryon multiplicity distributions are predicted to be sensitive to the properties of the nuclear matter created in high-energy nuclear collisions. In this talk, we present the collision centrality and acceptance (rapidity and transverse momentum) dependence of the ratio of the 6$^{\rm th}$- to the 2$^{\rm nd}$-order cumulant ratio ($C_{6}/C_{2}$) of net-proton in Au+Au collisions at $\sqrt{s_{\rm NN}}=54.4$ and 200 GeV measured by the STAR detector at RHIC. The new results are compared to hadron transport model and lattice QCD calculations.
We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant ($C_6/C_2$) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on $C_6/C_2$ of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract $C_6/C_2$ with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of $C_6/C_2$ is observed in central…
The proton, antiproton and mixed proton-antiproton factorial cumulants originating from the global conservation of baryon number are calculated analytically up to the sixth order. Our results can be directly tested in experiments.
We construct a multiplicity distribution characterized by large factorial cumulants (integrated correlation functions) from a simple combination of two ordinary multiplicity distributions characterized by small factorial cumulants. We find that such a model, which could be interpreted as representing two event classes, reproduces the preliminary data for the proton cumulants measured by the STAR collaboration at $7.7$ GeV very well. This model then predicts very large values for the fifth and sixth order factorial cumulants, which can be tested in experiment.
We analyze the behavior of cumulants of conserved charges in a subvolume of a thermal system with exact global conservation laws by extending a recently developed subensemble acceptance method (SAM) [V. Vovchenko et al., arXiv:2003.13905] to multiple conserved charges. Explicit expressions for all diagonal and off-diagonal cumulants up to sixth order that relate them to the grand canonical susceptibilities are obtained. The derivation is presented for an arbitrary equation of state with an arbitrary number of different conserved charges. The global conservation effects cancel out in any ratio …
We studied the effects of centrality fluctuation and deuteron formation on the cumulants ($C_n$) and correlation functions ($κ_n$) of protons up to sixth order in most central ($b<3$ fm) Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 3 GeV from a microscopic transport model (JAM). The results are presented as a function of rapidity acceptance within transverse momentum $0.4<p_{T}<2 $ GeV/$c$. We compared the results obtained by centrality bin width correction (CBWC) using charged reference particle multiplicity with CBWC done using impact parameter bins. It was found that at low energies the cen…
Fluctuations and correlations of conserved quantities (baryon number, strangeness, and charge) can be used to probe phases of strongly interacting QCD matter and the possible existence of a critical point in the phase diagram. The cumulants of the multiplicity distributions related to these conserved quantities are expected to be sensitive to possible increased fluctuations near a critical point and ratios of the cumulants can be directly compared to the ratios of the susceptibilities from Lattice QCD calculations. In these proceedings, the measurements of the cumulants of net-proton multiplic…
In studies of heavy-ion collisions, fluctuations of conserved quantities are considered as an important signal of the transition between the hadronic and partonic phases of nuclear matter. In this paper, it is investigated how the local charge conservation affects higher-order cumulants of net-charge distributions at LHC energies. Simple expressions for the cumulants are derived under the assumption that particle-antiparticle pairs are produced in local processes from sources that are nearly uncorrelated in rapidity. For calculations with these expressions, one needs to know only the second cu…
Fluctuations of conserved quantities such as net-baryon, net-charge, and net-strangeness numbers have generated considerable interest in the study of the thermodynamic properties of the hot and dense QCD matter. Theoretical calculations suggest that the off-diagonal cumulants of conserved charges along with the diagonal cumulants can help better constrain the freeze-out parameters and, therefore, help to map the QCD phase diagram. In this proceeding, we briefly outline the recent STAR measurements on the second-order off-diagonal cumulants of net-charge, net-proton, and net-kaon multiplicity d…
Finite-size behavior of higher-order cumulant ratios near criticality in two-dimensional Potts models
Indian Institute of Science Education and Research Bhopal（印度科学教育研究所博帕尔分校）；School of Physical Sciences, National Institute of Science Education and Research（国家科学教育研究所物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
Initial partonic eccentricities in Au+Au collisions at center-of-mass energy $\sqrt{s_{NN}}$ = 200 GeV are investigated using a multi-phase transport model with string melting scenario. The initial eccentricities in different order of harmonics are studied using participant and cumulant definitions. Eccentricity in terms of second-, fourth- and sixth order cumulants as a function of number of participant nucleons are compared systematically with the traditional participant definition. The ratio of the cumulant eccentricities $\varepsilon\left\{4\right\}/\varepsilon\left\{2\right\}$ and $\varep…
Cumulants of conserved charges fluctuations are regarded as a potential tool to study the criticality in the QCD phase diagram and to determine the freeze-out parameters in a model-independent way. At LHC energies, the measurements of the ratio of the net-baryon (net-proton) cumulants can be used to test the lattice QCD predictions. In this work, we present the first measurements of cumulants of the net-proton number distributions up to $4^{th}$ order in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 and 5.02 TeV as a function of collision centrality. We compare our cumulant ratios resul…
We report the collision-centrality dependence of cumulants of event-by-event net-proton, net-charge and net-kaon distributions in Au+Au collisions for center-of-mass energy $\sqrt{s_{NN}}$ = 54.4 GeV from the STAR experiment. Strong collision-centrality dependence is observed for cumulants ($C_{n}, n$ $\leq$ 4) of the net-particle distributions. The cumulant ratios $C_{3}/C_{2}$, $C_{4}/C_{2}$ and $C_{6}/C_{2}$ exhibit a weak collision-centrality dependence. The $C_{6}/C_{2}$ of net-proton and net-charge distributions for most central gold nuclei collisions at $\sqrt{s_{NN}}$ = 54.4 GeV show p…
Fluctuations of conserved quantities, such as baryon, electric charge and strangeness number, are sensitive observables in heavy-ion collisions to search for the QCD phase transition and critical point. In this paper, we performed a systematical analysis on the various cumulants and cumulant ratios of event-by-event net-strangeness distributions in Au+Au collisions at $\sqrt{s_{NN}}$=7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV from UrQMD model. We performed a systematical study on the contributions from various strange baryons and mesons to the net-strangeness fluctuations. The results demonstra…
We introduce a fast and simple method of computing cumulants of net-proton or net-charge fluctuations in event-by-event hydrodynamic simulations of heavy-ion collisions. One evaluates the mean numbers of particles in every hydrodynamic event. Cumulants are then expressed as a function of these mean numbers. We implement the corrections due to global conservation laws. The method is tested using ideal hydrodynamic simulations of Au+Au collisions at $\sqrt{s_{NN}}=200$ AGeV with the NeXSPheRIO code. Results are in good agreement with experimental data on net-proton and net-charge fluctuations by…
Fluctuations of conserved quantities are sensitive observables to probe the signature of QCD phase transition and critical point in heavy-ion collisions. With the UrQMD model, we have studied the centrality and energy dependence of various order cumulants and cumulant ratios (up to fourth order) of net-proton,net-charge and net-kaon multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}$= 7.7, 11.5, 19.6, 27, 39, 62.4, 200 GeV. The model results show that the production mechanism of the particles and anti-particles have significant impacts on the cumulants of net-particles multiplici…
We show that the effect of finite acceptance drastically influences the net-baryon and net-charge cumulants, which are believed to be sensitive probes of the QCD phase diagram. We derive the general formulae that relate the true cumulants K_{n} which reflect the full dynamics of the system with the actually measured cumulants c_{n} for a given acceptance, modeled by a binomial probability parameter p. We find that this relation involves additional moments which cannot be expressed by cumulants and should be measured in order to extract any potential information about the QCD critical point. We…
One of the main goals of the RHIC Beam Energy Scan (BES) program is to study the QCD phase structure, which includes the search for the QCD critical point, over a wide range of chemical potential. Theoretical calculations predict that fluctuations of conserved quantities, such as baryon number (B), charge (Q), and strangeness (S), are sensitive to the correlation length of the dynamical system. Experimentally, higher moments of multiplicity distributions have been utilized to search for the QCD critical point in heavy-ion collisions. In this paper, we report recent efficiency-corrected cumulan…
We propose a purity correction to subtract effects of combinatorial backgrounds from cumulants of hyperon number distributions. We argue that cumulants and mix-cumulants of sidebands, whose yield is comparable with that of background particles in the signal region, can be used for the correction. The method is demonstrated in a simple toy model by introducing effects of reconstruction efficiencies and backgrounds. We show that topological cut parameters for hyperon reconstructions can be optimized to achieve the best statistical significance after purity and efficiency corrections. The method …
We discuss the modification of the cumulants of the net baryon and net proton distributions due to the global conservation of baryon number in heavy-ion collisions. Corresponding probability distributions and their cumulants are derived analytically. We show that the conservation of baryon number results in a substantial decrease of higher order cumulants. Based on our studies, we propose an observable that is insensitive to the modifications due to baryon number conservation.
We present a systematic comparison between the recently measured cumulants of the net-proton distributions by STAR for 0-5% central Au+Au collisions at $\sqrt{s_{NN}}$=7.7-200 GeV and two kinds of possible baseline measures, the Poisson and Binomial baselines. These baseline measures are assuming that the proton and anti-proton distributions independently follow Poisson statistics or Binomial statistics. The higher order cumulant net-proton data are observed to deviate from all the baseline measures studied at 19.6 and 27 GeV. We also compare the net-proton with net-baryon fluctuations in UrQM…
We present a systematic procedure for analyzing cumulants to arbitrary order in the context of heavy-ion collisions. It generalizes and improves existing procedures in many respects. In particular, particles which are correlated are allowed to belong to different phase-space windows, which may overlap. It also allows for the analysis of cumulants at any order, using a simple algorithm rather than complicated expressions to be derived and coded by hand. In the case of azimuthal correlations, it automatically corrects to leading order for detector non-uniformity, and it is useful for numerous ot…
Measurements of anisotropic flow coefficients with two- and multi-particle cumulants for inclusive charged particles in Pb-Pb collisions at $\sqrt{{\textit s}_\text{NN}} = 5.02$ and 2.76 TeV are reported in the pseudorapidity range $|η| < 0.8$ and transverse momentum $0.2 < p_\text{T} < 50$ GeV/$c$. The full data sample collected by the ALICE detector in 2015 (2010), corresponding to an integrated luminosity of 12.7 (2.0) $μ$b$^{-1}$ in the centrality range 0-80%, is analysed. Flow coefficients up to the sixth flow harmonic ($v_6$) are reported and a detailed comparison among results at the tw…
We calculate the cumulants and correlation functions of net-kaon multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ GeV using a multiphase transport model (AMPT) with both a new coalescence mechanism and all charge conservation laws. The AMPT model can qualitatively describe the centrality dependences of the net-kaon cumulants and cumulant ratios measured by the STAR experiment. By focusing on the stage evolution of the cumulants, cumulant ratios, and correlation functions, we reveal several key effects on the fluctuations and correlations of strangeness during the dynamic…
In the search of QCD phase boundary and critical point, higher-order cumulants of conserved quantities are proposed as promising observables and have been studied extensively both experimentally and theoretically. In this paper we present cumulant ratios up to $6^{th}$-order of net-proton number distributions in Au+Au collisions at $\sqrt{\mathrm{s_{NN}}}$ = 7.7 - 200 GeV from STAR Beam Energy Scan program phase I and $\sqrt{\mathrm{s}}$ = 200 GeV $p+p$ collisions. The results are compared with various models and Lattice QCD calculations.
It is shown how high-order cumulants of net-charge distribution in hadronic collisions at LHC energies can be expressed via lower-order terms under the assumption that particle-antiparticle pairs are produced in independent local processes. It is argued and tested with HIJING model that this assumption is typically valid for net-proton fluctuations in the case when no critical behaviour is present in the system. Values estimated in such a way can be considered as baselines for direct measurements of high-order net-charge fluctuations in real data.
The multiplicity percentile dependence of cumulants, of net-proton number distributions in Au$-$Au collisions at $\sqrt{s_{NN}} = $ 200 GeV and Pb$-$Pb collisions at $\sqrt{s_{NN}} = $ 2.76 TeV has been investigated using the Angantyr model (the heavy-ion extension of the \textsc{Pythia 8} model). The effects of finite transverse momentum ($p_{\mathrm T}$) and pseudorapidity ($η$) acceptance on the net-proton cumulants have also been studied. Furthermore, the effects of the hydrodynamic expansion and feed down from weak decays were explored. It was found that radial flow has substantial impact…
The effects of volume corrections and resonance decays (the resulting correlations between positive charges and negative charges) on cumulants of net-proton distributions and net-charge distributions are investigated by using a Monte Carlo hadron resonance gas ({\tt MCHRG}) model. The required volume distributions are generated by a Monte Carlo Glauber ({\tt MC-Glb}) model. Except the variances of net-charge distributions, the {\tt MCHRG} model with more realistic simulations of volume corrections, resonance decays and acceptance cuts can reasonably explain the data of cumulants of net-proton …
We present new results on up to $6^{th}$ order cumulants of net baryon-number fluctuations at small values of the baryon chemical potential, $μ_B$, obtained in lattice QCD calculations with physical values of light and strange quark masses. Representation of the Taylor expansions of higher order cumulants in terms of the ratio of the two lowest order cumulants, $M_B/σ_B^2=χ_1^B(T,μ_B)/χ_2^B(T,μ_B)$, allows for a parameter free comparison with data on net proton-number cumulants obtained by the STAR Collaboration in the Beam Energy Scan at RHIC. We show that recent high statistics data on skewn…
We studied the centrality selection effect on cumulants (up to fourth order) and the cumulants ratios of net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 19.6 and 200 GeV from UrQMD model. The net-proton cumulants are calculated with collision centralities by using charged particle multiplicity from different pesudorapidity ($η$) region. By comparing the results from various collision centralities, we found that the autocorrelation effects are not significant in the results with collision centralities "refmult-3" and "refmult-2", which are using mid-…
We present the CBM physics performance study for measurements of the higher order cumulants of the net-proton multiplicity distributions. These observables are proxy for net-baryon fluctuations and are commonly used to study the phase structure of QCD phase diagram. The simulation is done for $Au+Au$ collision at beam kinetic energy $E_{lab} = 10$ AGeV. The cumulants of net-proton distributions have been calculated at midrapidity ($|Δy| =1$) for the transverse momentum range $0.2 < p_T < 2.0$ GeV/c. The centrality dependence of cumulants of net-proton upto order four is presented. The efficien…
We have studied the effect of limited statistics of data on measurement of the different order of cumulants of net-proton distribution assuming that the proton and antiproton distributions follow Possionian and Binomial distributions with initial parameters determined from experimental results for two top center of mass energies ($\sqrt{s_{\mathrm{NN}}}=200$ and $62.4$ GeV) in most central ($0-5$%) Au$+$Au collisions at Relativistic Heavy Ion Collider (RHIC). In this simulation, we observe that the central values for higher order cumulants have a strong dependence on event sample size and due …
Fluctuations of conserved quantities such as baryon number (B), electric charge number (Q), and strangeness number (S), are sensitive to the correlation length and can be used to probe non-gaussian fluctuations near the critical point. Experimentally, higher moments of the multiplicity distributions have been used to search for the QCD critical point in heavy-ion collisions. In this paper, we report the efficiency-corrected cumulants and their ratios of mid- rapidity (|y| < 0.5) net-kaon multiplicity distributions in Au+Au collisions at 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV collecte…
Higher-order cumulants of the distributions of conserved charges, such as net-baryon number, are sensitive to the quantum chromodynamics(QCD) phase transition and the QCD critical point. We calculate the cumulants and correlation functions of proton, antiproton, and net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ GeV using a multiphase transport model(AMPT). The AMPT model can basically describe the trends of cumulants, cumulant ratios, (normalized) correlation functions of the proton and net-proton measured by the STAR experiment. The multiproton (baryon) co…
With the help of transport and statistical models, we find that the ratios of higher net-proton cumulants measured at RHIC are dominated by the statistical fluctuations. Future measurements should focus on the dynamical fluctuations, which are relevant to the underlying mechanisms of particle production, the critical phenomena in particular. We also demonstrate that a proton-antiproton correlation directly show if protons and antiprotons are emitted independently.
We study the effects of correlations on cumulants and their ratios of net-proton multiplicity distributions which have been measured for central (0\%-5\%) Au + Au collisions at the Relativistic Heavy Ion Collider (RHIC). This effect has been studied assuming individual proton and anti-proton distributions as a Poisson or Negative Binomial Distribution (NBD). In-spite of significantly correlated production due to baryon number, electric charge conservation and kinematical correlations of protons and anti-protons, the measured cumulants of the net-proton distribution follow the independent produ…
We modify the usual definitions of cumulants of net-charge fluctuations in a way that isolates dynamical fluctuations. The new observables, which we call dynamical cumulants, are robust with respect to trivial correlations induced by volume fluctuations and global charge conservation. We illustrate the potential of dynamical cumulants by carrying out Monte Carlo simulations where all correlations are trivial. The results of our simulations agree well with Relativistic Heavy Ion Collider (RHIC) data, and are used to illustrate that dynamical cumulants consistently isolate dynamical fluctuations…
We analyze the rapidity and transverse momentum dependence for the cumulants of the net-proton and net-baryon distributions in Au+Au collisions at $\sqrt{s_{\text{NN}}} = 5\,\text{GeV}$ with a microscopic hadronic transport (JAM) model. To study the effects of mean field potential and softening of equation of state (EoS) on the fluctuations of net-proton (baryon) in heavy-ion collisions, the calculations are performed with two different modes. The softening of EoS is realized in the model by implementing the attractive orbit in the two-body scattering to introduce a reduction pressure of the s…
Fluctuations and correlations of conserved charges are sensitive observables for studying the QCD phase transition and critical point in high-energy heavy-ion collisions. We have studied the centrality and energy dependence of mixed-cumulants (up to fourth order) between net-baryon and net-strangeness in Au+Au collisions at $\sqrt{s_{NN}}$= 7.7, 11.5, 19.6, 27, 39, 62.4, 200 GeV from UrQMD model. To compare with other theoretical calculations, we normalize these mixed-cumulants by various order cumulants of net-strangeness distributions. We found that the results obtained from UrQMD calculatio…
Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Lorentz-covariant treatment of nuclear mean-field potential is considered, the fluctuations of net-baryon, net-charge and deuterons multiplicity distributions in Au+Au head-on collisions at $\sqrt{s_{NN}}=3.0-5.0$ GeV are calculated. The results show that the nuclear mean-field potential can significantly enhance the magnitude of baryon number fluctuations in narrow rapidity windows, and this enhancement rapidly weakens with increasing beam energy. However, for proton and net-charge number fluctuations, the me…
Azimuthal angle correlations of charged hadrons were measured in $\sqrt s_{NN}$ = 2.76 TeV PbPb collisions by the CMS experiment. The distributions exhibit anisotropies that are correlated with the event-by-event orientation of the reaction plane. Several methods were employed to extract the strength of the signal: the event-plane, cumulant and Lee-Yang Zeros methods. These methods have different sensitivity to correlations that are not caused by the collective motion in the system (non-flow correlations due to jets, resonance decays, and quantum correlations). The second Fourier coefficient o…
We investigate the time evolution of higher order cumulants of conserved charges in a volume with the diffusion master equation. Applying the result to the diffusion of non-Gaussian fluctuations in the hadronic stage of relativistic heavy ion collisions, we show that the fourth-order cumulant of net-electric charge at LHC energy is suppressed compared with the recently observed second-order cumulant at ALICE, if the higher order cumulants at hadronization are suppressed compared with their values in the hadron phase in equilibrium. The significance of the experimental information on the rapidi…
I investigate the volume corrections on cumulants of total charge distributions and net proton distributions. The required volume information is generated by an optical Glauber model. I find that the corrected statistical expectations of multiplicity distributions mimic the negative binomial distributions at non-central collisions, and they tend to approach the Poisson ones at most-central collisions due to the "boundary effects," which suppress the volume corrections. However, net proton distributions and reference multiplicity distributions are sensitive to the external volume fluctuations a…
First experimental results are presented on event-by-event net-proton fluctuation measurements in Pb- Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV, recorded by the ALICE detector at the CERN LHC. The ALICE detector is well suited for such studies due to its excellent particle identification capabilities and large acceptance, which is crucial for fluctuation analysis. The studies are focussed on second order cumulants, but the analysis technique used is more general and will be applied, in the near future, also to higher order cumulants.
We determine the net-baryon multiplicity distribution which reproduces all cumulants measured so far by lattice QCD. We present the dependence on the volume and temperature of this distribution. We find that for temperatures and volumes encountered in heavy ion reactions, the multiplicity distribution is very close to the Skellam distribution, making the experimental determination of it rather challenging. We further provide estimates for the statistics required to measure cumulants of the net-baryon and net-proton distributions.
